TORONTO (Reuters) - Unitholders of Milestone Apartments Real Estate Investment Trust MST_u.TO have approved the takeover of the company by U.S. private investment firm Starwood Capital Group for about $1.3 billion, according to people familiar with the situation.

The move comes after Starwood agreed with Milestone last week to a sweetened offer of $16.25 per Milestone unit. Milestone had initially, in January, agreed to be bought out by Starwood in an all-cash transaction.

Close to 70 percent of Milestone unitholders who voted were in favor of the transaction, based on early voting figures, the people said, declining to be named as the matter is private. The transaction needed the approval of two-thirds of Milestone unitholders.

Dallas-based Milestone declined comment.

Milestone, which went public in Toronto in 2013, owns and manages apartment properties targeting blue-collar workers across the U.S. Southeast and Southwest.